Masatomo Sawahara

Masatomo Sawahara
Hirosaki University · Faculty of Education

PhD

About

12
Publications
493
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7
Citations
Introduction
Skills and Expertise
Additional affiliations
April 2022 - March 2023
Saitama University
Position
  • PostDoc Position (Part-time researcher)
Education
April 2019 - March 2022
Saitama University
Field of study
  • Algebraic Geometry
April 2017 - March 2019
Saitama University
Field of study
  • Algebraic Geometry
April 2013 - March 2017
Saitama University
Field of study

Publications

Publications (12)
Article
Full-text available
In this article, we shall look into the existence of vertical cylinders contained in a weak del Pezzo fibration as a generalization of the former work of Dubouloz and Kishimoto in which they observed vertical cylinders found in del Pezzo fibrations. With the essence lying in the existence of a cylinder in the generic fiber, we devote ourselves main...
Preprint
Full-text available
Let $S$ be a del Pezzo surface with at worse Du Val singularities of degree $\ge 3$. We construct an $H$-polar cylinder for any ample $\mathbb{Q}$-divisor $H$ on $S$.
Article
Full-text available
Cylinders in projective varieties play an important role in connection with unipotent group actions on certain affine algebraic varieties. The previous work due to Dubouloz and Kishimoto deals with the condition for a del Pezzo fibration to contain a vertical cylinder. In the present work, as a generalization in the sense of singularities, we shall...
Preprint
Full-text available
We consider minimal compactifications of the complex affine plane. Minimal compactifications of the affine plane with at most log canonical singularities are classified. Moreover, every minimal compactification of the affine plane with at most log canonical singularities has only star-shaped singular points. In this article, we classify minimal com...
Article
We give the classification of normal del Pezzo surfaces of rank one with at most log canonical singularities containing the affine plane defined over an algebraically nonclosed field of characteristic zero. As an application, we have a criterion for del Pezzo fibrations with canonical singularities whose generic fibers are not smooth to contain ver...
Article
Full-text available
We shall consider minimal analytic compactifications of the affine plane with singularities. In previous work, Kojima and Takahashi proved that any minimal analytic compactification of the affine plane, which has at worse log canonical singularities, is a numerical del Pezzo surface (i.e., a normal complete algebraic surface with the numerically am...
Preprint
Full-text available
We shall consider minimal analytic compactifications of the affine plane with singularities. In previous work, Kojima and Takahashi proved that any minimal analytic compactification of the affine plane, which has at worse log canonical singularities, is a numerical del Pezzo surface (i.e., a normal complete algebraic surface with the numerically am...
Article
Full-text available
A Zariski open subset of an algebraic variety is called a cylinder if it is isomorphic to the direct product of the affine line and an algebraic variety. We consider the existing condition of relative cylinders with respect to a projective dominant morphism of relative dimension two. Since this consideration is essentially a determination of the ex...
Preprint
Full-text available
In this article, we determine the existing condition of cylinders in smooth minimal geometrically rational surfaces over a perfect field. Furthermore, we show that for any birational map between smooth projective surfaces, one contains a cylinder if and only if so does the other.
Preprint
Full-text available
In this article, we give the classification of normal del Pezzo surfaces of rank one with at most log canonical singularities containing the affine plane defined over an algebraically non-closed field of characteristic zero. As an application, we have a criterion for del Pezzo fibrations with canonical singularities whose generic fibers are not smo...
Preprint
Full-text available
Cylinders in projective varieties play an important role in connection with unipotent group actions on certain affine algebraic varieties. The previous work due to Dubouloz and Kishimoto deals with the condition for a del Pezzo fibration to contain a vertical cylinder. In the present work, as a generalization in the sense of singularities, we shall...
Preprint
Full-text available
In this article, we shall look into the existence of vertical cylinders contained in a weak del Pezzo fibration as a generalization of the former work due to Dubouloz and Kishimoto in which they observed that of vertical cylinders found in del Pezzo fibrations. The essence lying in the existence of a cylinder in the generic fiber, we devote mainly...